What is the compound interest on a sum of Rs. 12,500 at 15% p.a. in 2 years, if the interest is compounded 8-monthly?

Correct — B. Rescale the annual rate and the time to 8-month periods.

Rate per period = 15% × 8⁄12 = 10%
Periods = 24 months ÷ 8 = 3

Amount = 12,500 × 1.1³
= 12,500 × 1.331 = 16,637.50

CI = 16,637.50 − 12,500 = ₹4,137.50 → option (b)

Why the others are wrong

• (a)
  4100 — 4,100 is 32.8% of 12,500, which needs a growth factor of 1.328. Three periods at 10% give 1.1³ = 1.331.
• (c)
  4000 — 4,000 is below even annual compounding, 12,500 × 1.15² − 12,500 = ₹4,031.25. Compounding more often at the same annual rate only adds interest.
• (d)
  4200 — 4,200 exceeds half-yearly compounding, 12,500 × 1.075⁴ − 12,500 ≈ ₹4,193.36. An 8-month period is longer than 6 months, so it must earn less.

When interest is compounded every k months, rescale both the rate and the time: rate per period = annual rate × k⁄12, and the number of periods = total months ÷ k.

Here 8 divides 24 exactly, so there are 3 whole periods at 10%, and 1.1³ = 1.331 does the rest.

Key facts

• Compounded every k months: rate per period = annual rate × k⁄12.
• Number of periods = total months ÷ k.
• 1.1³ = 1.331, so three periods at 10% add 33.1% to the principal.
• At the same annual rate, more frequent compounding gives more interest.

Common traps

• Using 15% for each 8-month period: 12,500 × 1.15³ − 12,500 ≈ ₹6,511, far above every option.
• Ignoring the 8-monthly clause and compounding annually: that gives ₹4,031.25, which is not an option.
• Stopping at the amount, ₹16,637.50: the question asks for the interest.

No directly related past PYQ was found.